几种特殊模糊二元关系的探讨

Discussion about several particular fuzzy binary relations

讨论了竞赛,全序,偏序,弱序,拟序,严格全序,严格偏序,严格弱序八种特殊的二元关系,指出了它们之间的联系。如全序关系一定是弱序关系,弱序关系一定是拟序关系等;以T,S三角模算子为基础,在T非对称,S强完全,T传递,S负传递这些概念的基础上,分别给出了模糊竞赛,模糊全序,模糊偏序,模糊弱序,模糊拟序,模糊严格全序,模糊严格偏序,模糊严格弱序关系的定义,并讨论了它们之间的联系,如T-S全序一定是T-S弱序,T-S弱序一定是T拟序等,得出了与普通情形下相一致的结论。

Eight particular binary relations （ tournament, total order, partial order, weak order, quasi order. strict total order, strict partial order, strict weak order） have been discussed, and the relationship between them have been pointed out. Meanwhile, based on the T,S triangular norms, definitions of the eight particular fuzzy binary relations （fuzzy tournament, fuzzy total order, fuzzy partial order, fuzzy weak order, fuzzy quasi order, fuzzy strict total order, fuzzy strict partial order, fuzzy strict weak order） have been given respectively, and the relationship between them have been discussed. In the end, it is found that the conclusion in fuzzy case is consistent with crisp case.